Logarithmically Convex Function

A function $f(x)$ is logarithmically convex on the interval $[a,b]$ if $f>0$ and $\ln f(x)$ is Concave on $[a,b]$. If $f(x)$ and $g(x)$ are logarithmically convex on the interval $[a,b]$, then the functions $f(x)+g(x)$ and $f(x)g(x)$ are also logarithmically convex on $[a,b]$.

See also Convex Function

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1100, 1980.